Binomial Theorem · NDA previous year questions

2014 9 questions

1. Q122014 · 28 Sept 2014

   For the next five (05) items that follow : Consider the expansion ${\left(x^2+\frac{1}{x}\right)}^{15}$. What is the independent term in the given expansion ?

   1. A.2103
   2. B.3003
   3. C.4503
   4. D.None of the above
   Show answer

   Answer: B

2. Q132014 · 28 Sept 2014

   For the next five (05) items that follow : Consider the expansion ${\left(x^2+\frac{1}{x}\right)}^{15}$. What is the ratio of coefficient of $x^{15}$ to the term independent of x in the given expansion ?

   1. A.1
   2. B.$1/2$
   3. C.$2/3$
   4. D.$3/4$
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   Answer: A

3. Q142014 · 28 Sept 2014

   For the next five (05) items that follow : Consider the expansion ${\left(x^2+\frac{1}{x}\right)}^{15}$. Consider the following statements : 1. There are 15 terms in the given expansion. 2. The coefficient of $x^{12}$ is equal to that of $x^3$. Which of the above statements is/are correct ?

   1. A.1 only
   2. B.2 only
   3. C.Both 1 and 2
   4. D.Neither 1 nor 2
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   Answer: B

4. Q152014 · 28 Sept 2014

   For the next five (05) items that follow : Consider the expansion ${\left(x^2+\frac{1}{x}\right)}^{15}$. Consider the following statements : 1. The term containing $x^2$ does not exist in the given expansion. 2. The sum of the coefficients of all the terms in the given expansion is $2^{15}$. Which of the above statements is/are correct ?

   1. A.1 only
   2. B.2 only
   3. C.Both 1 and 2
   4. D.Neither 1 nor 2
   Show answer

   Answer: C

5. Q162014 · 28 Sept 2014

   For the next five (05) items that follow : Consider the expansion ${\left(x^2+\frac{1}{x}\right)}^{15}$. What is the sum of the coefficients of the middle terms in the given expansion ?

   1. A.$C(15,9)$
   2. B.$C(16,9)$
   3. C.$C(16,8)$
   4. D.None of the above
   Show answer

   Answer: C

6. Q562014 · 28 Sept 2014

   For the next three (03) items that follow : Consider the function $f(x)=\{\begin{array}{ll}{x}^2-5,& x\le 3\\ \sqrt{x+13},& x>3\end{array}$ What is the differential coefficient of $f(x)$ at $x=12$?

   1. A.5/2
   2. B.5
   3. C.1/5
   4. D.1/10
   Show answer

   Answer: D

7. Q202014 · 20 Apr 2014

   For the next three (03) items that follow: In the expansion of ${\left(x^3-\frac{1}{x^2}\right)}^n$ where $n$ is a positive integer, the sum of the coefficients of $x^5$ and $x^{10}$ is 0. What is $n$ equal to?

   1. A.5
   2. B.10
   3. C.15
   4. D.None of the above
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   Answer: C

8. Q212014 · 20 Apr 2014

   For the next three (03) items that follow: In the expansion of ${\left(x^3-\frac{1}{x^2}\right)}^n$ where $n$ is a positive integer, the sum of the coefficients of $x^5$ and $x^{10}$ is 0. What is the value of the independent term?

   1. A.5005
   2. B.7200
   3. C.$-5005$
   4. D.$-7200$
   Show answer

   Answer: C

9. Q222014 · 20 Apr 2014

   For the next three (03) items that follow: In the expansion of ${\left(x^3-\frac{1}{x^2}\right)}^n$ where $n$ is a positive integer, the sum of the coefficients of $x^5$ and $x^{10}$ is 0. What is the sum of the coefficients of the two middle terms?

   1. A.0
   2. B.1
   3. C.$-1$
   4. D.None of the above
   Show answer

   Answer: A